This invention relates to investigation of earth formations and, more particularly, to a method and apparatus for determining properties of earth formations using sonic well logging which can characterize earth formations exhibiting complex acoustic behavior, and to a method and apparatus for determining radial variations in shear slownesses of earth formations surrounding a borehole.
It is well known that mechanical disturbances can be used to establish acoustic waves in earth formations surrounding a borehole, and the properties of these waves can be measured to obtain important information about the formations through which the waves have propagated. Parameters of compressional, shear and Stoneley waves, such as their velocity (or its reciprocal, slowness) in the formation and in the borehole, can be indicators of formation characteristics that help in evaluation of the location and/or producibility of hydrocarbon resources.
An example of a logging device that has been used to obtain and analyze sonic logging measurements of formations surrounding an earth borehole is called a Dipole Shear Sonic Imager (xe2x80x9cDSIxe2x80x9dxe2x80x94trademark of Schlumberger), and is of the general type described in Harrison et al., xe2x80x9cAcquisition and Analysis of Sonic Waveforms From a Borehole Monopole And Dipole Source For The Determination Of Compressional And Shear Speeds And Their Relation To Rock Mechanical Properties And Surface Seismic Dataxe2x80x9d, Society of Petroleum Engineers, SPE 20557, 1990. In conventional use of the DSI logging tool, one can present compressional slowness, xcex94tc, shear slowness, xcex94ts, and Stoneley slowness, xcex94tst, each as a function of depth, z. [Slowness is the reciprocal of velocity and corresponds to the interval transit time typically measured by sonic logging tools.]
An acoustic source in a fluid-filled borehole generates headwaves as well as relatively stronger borehole-guided modes. A standard sonic measurement system consists of placing a piezoelectric source and an hydrpohone receivers inside a fluid-filled borehole. The piezoelectric source is configured in the form of either a monopole or a dipole source. The source bandwidth typically ranges from a 0.5 to 20 kHz. A monopole source generates primarily the lowest-order axisymmetric mode, also referred to as the Stoneley mode, together with compressional and shear headwaves. In contrast, a dipole source primarily excites the lowest-order flexural borehole mode together with compressional and shear headwaves. The headwaves are caused by the coupling of the transmitted acoustic energy to plane waves in the formation that propagate along the borehole axis. An incident compressional wave in the borehole fluid produces critically refracted compressional waves in the formation. Those refracted along the borehole surface are known as compressional headwaves. The critical incidence angle xcex8i=sinxe2x88x921(Vf/Vc), where Vf is the compressional wave speed in the borehole fluid; and Vc is the compressional wave speed in the formation. As the compressional headwave travels along the interface, it radiates energy back into the fluid that can be detected by hydrophone receivers placed in the fluid-filled borehole. In fast formations, the shear headwave can be similarly excited by a compressional wave at the critical incidence angle xcex8i=sinxe2x88x921(Vf/Vs), where Vs is the shear wave speed in the formation. It is also worth noting that headwaves are excited only when the wavelength of the incident wave is smaller than the borehole diameter so that the boundary can be effectively treated as a planar interface. In a homogeneous and isotropic model of fast formations, as above noted, compressional and shear headwaves can be generated by a monopole source placed in a fluid-filled borehole for determining the formaton compressional and shear wave speeds. It is known that refracted shear headwaves cannot be detected in slow formations (where the shear wave velocity is less than the borehole-fluid compressional velocity) with receivers placed in the borehole fluid. In slow formations, formation shear velocities are obtained from the low-frequency asymptote of flexural dispersion. There are standard processing techniques for the estimation of formation shear velocities in either fast or slow formations from an array of recorded dipole waveforms.
Typically, the subsurface formations are considered to be homogeneous and isotropic material, where the compressional and shear velocities, Vc and Vs, of the formations are only a function of depth. It is known, however, that formations can be anisotropic, where the compressional and shear slownesses are a function of azimuth, xcex8. Anisotropy can occur, for example because of layered shales, aligned fractures or differences in the magnitudes of the principle stresses in the formations. It is also known that formations may be inhomogeneous, where the slownesses become a function of radial distance, r, from the borehole. Inhomogeneity can be caused, for example, by mud-shale interactions or by mechanical damage due to stress concentrations. It was among the objectives of the invention of the parent application hereof (the above-referenced copending U.S. patent application Ser. No. 09/741,574) to provide an improved technique for characterizing earth formations exhibiting complex acoustic behavior. A technique of that invention included outputting a characterization of the formation as one of the following types: isotropic/homogeneous, anisotropic/homogeneous, isotropic/inhomogeneous, and anisotropic/inhomogeneous.
As also described in the above-referenced copending patent application, a technique can be used for determining homogeneity/inhomogeneity of a formation by comparing measured and model dispersion curves. The model data can be produced, for example, from measured compressional and shear velocities, formation mass density, mud density, mud compressional velocity, and borehole diameter (see B. Sinha, A. Norris, and S. Chang, Borehole Flexural Modes In Anisotropic Formations, Geophysics, 59, 1037-1052, 1994). If the measured data superimposes with the model data, it can be concluded that the formation is homogeneous. When the measured data deviates at high frequency, it can be concluded that the formation is inhomogeneous. When the deviation occurs at high frequencies (corresponding to probing near to the borehole), such deviation indicates that there is inhomogeneity or damage near the borehole surface. Accordingly, useful technique has been set forth for determining, at least qualitatively, the presence of near-borehole inhomogeneity; that is, the presence of phenomena such as mechanical damage in formations subject to tectonic stresses which cause radial variation in shear slownesses. However, it would be very useful to have an accurate quantitative radial profile of shear slownesses that can be employed in the evaluation of formations for the presence and/or producibility of hydrocarbons. It is among the objects of the present invention to provide a method and apparatus that addresses this need in the well logging art.
The present invention is directed to a method and apparatus for determining radial variations in shear slownesses; in other words, a radial profile of shear slowness or velocity. In accordance with an embodiment of the technique of the invention, there is disclosed a method for determining a radial profile of sonic shear velocity of formations surrounding a fluid-containing borehole, comprising the following steps: suspending a logging device in the borehole; transmitting sonic energy from the logging device to establish flexural waves in the formation; receiving, at the logging device, sonic energy from the flexural waves, and producing from the received sonic energy, measurement signals at a number of frequencies; determining, at each of said number of frequencies, the flexural wave velocity in the formation; deriving sonic compressional and shear velocities of the substantially undisturbed formation; deriving sonic compressional velocity of the borehole fluid; and determining the radial profile of sonic shear velocity from the derived compressional and shear velocities of the substantially undisturbed formation, the derived compressional velocity of the borehole fluid, and the flexural wave velocities at said number of frequencies.
In an embodiment of the invention, the method further comprises deriving the ratio of formation mass bulk density to borehole fluid mass density, and the radial profile of sonic shear velocity is determined from the derived compressional and shear velocities of the substantially undisturbed formation, the derived compressional velocity of the borehole fluid, the derived ratio of formation mass bulk density to borehole fluid mass density, and the flexural wave velocities at said number of frequencies. In this embodiment, the method also comprises the steps of deriving a dispersion function from the flexural wave velocities at said number of frequencies, and deriving a reference dispersion function from said derived sonic compressional and shear velocities of the substantially undisturbed formation and the derived ratio of formation mass bulk density to borehole fluid mass density, and determining, at selected frequencies, the differences between velocities obtained from the dispersion function and the reference dispersion function, the radial profile of sonic shear velocity being determined from said differences. Further in this embodiment, the method includes the step of deriving, at said selected frequencies, the fractional changes in flexural velocity, from the respective ratios of said differences to said velocities obtained from the reference dispersion function, the radial profile of sonic shear velocity being determined from said fractional changes in flexural velocity.
The present invention can be employed, inter alia, for assisting completion strategies relating to casing and/or perforation decisions.
Further features and advantages of the invention will become more readily apparent from the following detailed description when taken in conjunction with the accompanying drawings.